We conducted a search for technosignatures in 2018 and 2019 April with the L-band receiver (1.15-1.73 GHz) of the 100 m diameter Green Bank Telescope. These observations focused on regions surrounding 31 Sun-like stars near the plane of the Galaxy. We present the results of our search for narrowband signals in this data set, as well as improvements to our data processing pipeline. Specifically, we applied an improved candidate signal detection procedure that relies on the topographic prominence of the signal power, which nearly doubles the signal detection count of some previously analyzed data sets. We also improved the direction-of-origin filters that remove most radio frequency interference (RFI) to ensure that they uniquely link signals observed in separate scans. We performed a preliminary signal injection and recovery analysis to test the performance of our pipeline. We found that our pipeline recovers 93% of the injected signals over the usable frequency range of the receiver and 98% if we exclude regions with dense RFI. In this analysis, 99.73% of the recovered signals were correctly classified as technosignature candidates. Our improved data processing pipeline classified over 99.84% of the ∼26 million signals detected in our data as RFI. Of the remaining candidates, 4539 were detected outside of known RFI frequency regions. The remaining candidates were visually inspected and verified to be of anthropogenic nature. Our search compares favorably to other recent searches in terms of end-to-end sensitivity, frequency drift rate coverage, and signal detection count per unit bandwidth per unit integration time.